Question

$\huge\mathrm{Question}$

⭐ A postage stamp kept below a rectangular glass slab of refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass slab.

⭐ The bob of a simple pendulum is imparted a velocity of 5 m/s¹ when it is at its mean position. To what maximum vertical height will it raise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air ? ( Take g = 10 m/s² ) ​

Answer 1

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Answer 2

Explanation:

$\huge\boxed{\fcolorbox{red}{purple}{QUESTION}}$

A postage stamp kept below a rectangular glass slab of refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass slab.

${\huge{\bold{\underline{\underline{Answer:}}}}}$

ʀᴇғʀᴀᴄᴛɪᴠᴇ ɪɴᴅᴇx ᴏғ ᴛʜᴇ ɢʟᴀss ʙʟᴏᴄᴋ, μɢ = 1.5

sʜɪғᴛ ɪɴ ᴛʜᴇ ɪᴍᴀɢᴇ = 7ᴍᴍ ᴏʀ 0.7 ᴄᴍ

ᴛʜɪᴄᴋɴᴇss ᴏғ ɢʟᴀss ʙʟᴏᴄᴋ ᴏʀ ʀᴇᴀʟ ᴅᴇᴘᴛʜ =?

sʜɪғᴛ = ʀᴇᴀʟ ᴅᴇᴘᴛʜ × (1 - 1/μ) 0.7

= ʀ × (1 - 1/1.5) ʀ

= 0.7 x 1.5/0.5 = 2.1ᴄᴍ

$\huge\boxed{\fcolorbox{red}{purple}{QUESTION}}$

The bob of a simple pendulum is imparted a velocity of 5 m/s¹ when it is at its mean position. To what maximum vertical height will it raise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air ? ( Take g = 10 m/s² )

${\huge{\bold{\underline{\underline{Answer:}}}}}$

ᴡʜᴇɴ ɪᴛ ɪs ᴀᴛ ᴍᴇᴀɴ ᴘᴏsɪᴛɪᴏɴ ɪᴛ ᴡɪʟʟ ʜᴀᴠᴇ ᴀ ᴋ.ᴇ ᴏғ 0.5ᴍᴠ^2

ᴋ.ᴇ =0.5 ×ᴍ×5×5 = 12.5×ᴍᴊ

60% ᴏғ ᴛʜɪs ᴋ.ᴇ ɪs ʟᴏsᴛ ʜᴇɴᴄᴇ ʀᴇᴍᴀɪɴɪɴɢ ɪs ᴇǫᴜᴀʟ ᴛᴏ (40/100)112.5×ᴍ= 5ᴍ

ᴘ.ᴇ = ᴍɢʜ = 5×ᴍ

ʜ = 5/ɢ = 5/10 = 0.5ᴍ

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@Gurjari